This paper presents an improved model of fluid inflow into hydraulic fractures. We also suggest here formulae for calculating flow rate in a horizontal well after multi-stage hydraulic fracturing job as dependent on the number of fractures, the angle of fracture deviation fr om the normal line to the horizontal section of the well and on the values of fractures’ dimensionless conductivity F_{cd}. In our previous papers we accounted for infinite conductivity, but only partially. In this paper we estimate the impact of fracture conductivity onto the total flow rate in a horizontal well after multi-stage hydraulic fracturing. The hydraulic fracture is viewed as a wedge-like channel with half-length of x_{f}, average width of w and constant height of h that is filled evenly with proppant and deviates at an angle ± from the normal line. Our assumption was that the pressure at fracture tip is higher than bottom-hole pressure p_{тр}> p_{з}, while the pressure at the beginning of the fracture (the point wh ere it enters the wellbore) is equal to bottom-hole pressure p_{з}. For F_{cd}>10 the previous and the current models render equal results. The new model is a powerful enabler for optimization of multi-stage fracturing it terms of identifying economically efficient number of ports as well as fracture half-length and the angle of fracture deviation from the normal line to the well.

References

1. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M.V., Flowrate calculation

model for fractured horizontal well depending on frac stages number

(In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 1, pp. 64–67.

2. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M.V., The model for rapid

calculation of horizontal well production rate depending on the number of

hydraulic fractures with anisotropic layer (In Russ.), Inzhenernaya praktika,

2016, no. 7, pp. 82–88.

3. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M.V., Consideration of

the impact of fracktures deviation from their perpendicular position to a horizontal

well on the liquid flow rate following a multi-stage hydraulic fracturing

(In Russ. ), Neftepromyslovoe delo, 2016, no. 10, pp. 37–42.

4. Cinco-L.H., Samaniego-V.F., Dominguex N., Transient pressure behavior for

a well with a finite-conductivity vertical fracture, SPE 6014-PA, 1978.

This paper presents an improved model of fluid inflow into hydraulic fractures. We also suggest here formulae for calculating flow rate in a horizontal well after multi-stage hydraulic fracturing job as dependent on the number of fractures, the angle of fracture deviation fr om the normal line to the horizontal section of the well and on the values of fractures’ dimensionless conductivity F_{cd}. In our previous papers we accounted for infinite conductivity, but only partially. In this paper we estimate the impact of fracture conductivity onto the total flow rate in a horizontal well after multi-stage hydraulic fracturing. The hydraulic fracture is viewed as a wedge-like channel with half-length of x_{f}, average width of w and constant height of h that is filled evenly with proppant and deviates at an angle ± from the normal line. Our assumption was that the pressure at fracture tip is higher than bottom-hole pressure p_{тр}> p_{з}, while the pressure at the beginning of the fracture (the point wh ere it enters the wellbore) is equal to bottom-hole pressure p_{з}. For F_{cd}>10 the previous and the current models render equal results. The new model is a powerful enabler for optimization of multi-stage fracturing it terms of identifying economically efficient number of ports as well as fracture half-length and the angle of fracture deviation from the normal line to the well.

References

1. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M.V., Flowrate calculation

model for fractured horizontal well depending on frac stages number

(In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 1, pp. 64–67.

2. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M.V., The model for rapid

calculation of horizontal well production rate depending on the number of

hydraulic fractures with anisotropic layer (In Russ.), Inzhenernaya praktika,

2016, no. 7, pp. 82–88.

3. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M.V., Consideration of

the impact of fracktures deviation from their perpendicular position to a horizontal

well on the liquid flow rate following a multi-stage hydraulic fracturing

(In Russ. ), Neftepromyslovoe delo, 2016, no. 10, pp. 37–42.

4. Cinco-L.H., Samaniego-V.F., Dominguex N., Transient pressure behavior for

a well with a finite-conductivity vertical fracture, SPE 6014-PA, 1978.